Spectral properties and classical decays in quantum open systems

García-Mata, Ignacio; Saraceno, Marcos

doi:10.1103/physreve.69.056211

Cited by 17 publications

(31 citation statements)

References 52 publications

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“…When the pair of states are obtained by the unitary evolution of slightly different hamiltonians from the same initial state, the behaviour in time of C AB reflects the regular or chaotic nature of the underlying classical motion [2,3,4]. If the states are related by a unitary transformation generated by an Hermitian operatorK,…”

Section: Phase Space Correlationsmentioning

confidence: 99%

Pure state correlations: chords in phase space

Almeida

Vallejos

Saraceno

2005

J. Phys. A: Math. Gen.

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The intensity of the overlap of a quantum state with all its phase space translations defines its quantum correlations. In the case of pure states, these are invariant with respect to Fourier transformation. The overlaps themselves are here studied in terms of the Wigner function and its Fourier transform, i.e., the characteristic function or chord function. Unlike the Wigner function, the chord function need not be real, but eventual symmetry with respect to reflections about a phase space point may relate these representations. Semiclassical approximations for the "classical-like" region of small chords and for large chords are derived. These lead to an interpretation of the Fourier invariance in terms of conjugate chords. The interrelation of large and small (sub-Planck) phase space structures previously noted in the literature are thus reinterpreted.

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Section: Phase Space Correlationsmentioning

confidence: 99%

Pure state correlations: chords in phase space

Almeida

Vallejos

Saraceno

2005

J. Phys. A: Math. Gen.

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“…This régime was already studied in various semiclassical approaches to study convergence to equilibrium in a quantum system subject to some type of noise (see e.g. results regarding the spectrum of noisy quantum propagators [12,40,43,27], the rate of decoherence [44,6,28] and its relation with quantum dynamical entropy [1,2,5]). …”

Section: Introductionmentioning

confidence: 99%

Relaxation Time of Quantized Toral Maps

Fannjiang

Nonnenmacher

Wołowski

2006

Ann. Henri Poincaré

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Abstract. We introduce the notion of the relaxation time for noisy quantum maps on the 2d-dimensional torus -a generalization of previously studied dissipation time. We show that relaxation time is sensitive to the chaotic behavior of the corresponding classical system if one simultaneously considers the semiclassical limit ( → 0) together with the limit of small noise strength (ǫ → 0).Focusing on quantized smooth Anosov maps, we exhibit a semiclassical régime < ǫ E ≪ 1 (where E > 1) in which classical and quantum relaxation times share the same asymptotics: in this régime, a quantized Anosov map relaxes to equilibrium fast, as the classical map does. As an intermediate result, we obtain rigorous estimates of the quantum-classical correspondence for noisy maps on the torus, up to times logarithmic in −1 . On the other hand, we show that in the "quantum régime" ǫ ≪ ≪ 1, quantum and classical relaxation times behave very differently. In the special case of ergodic toral symplectomorphisms (generalized "Arnold's cat" maps), we obtain the exact asymptotics of the quantum relaxation time and precise the régime of correspondence between quantum and classical relaxations.

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“…Following recent works [12,13,14,16,17,28,29] we study the effect of the dissipative noise channel described in Sec. V when composed with a unitary map.…”

Section: Composition With a Unitary Processmentioning

confidence: 99%

“…Diffusive noise in the form of a RUP was studied in [13,14,17], as a Gaussian sum of (normalized) translations in phase space. When composed with a unitary map the whole noisy map can be interpreted as a coarse graining [14,17] of the original map.…”

Section: A Random Unitary Processesmentioning

confidence: 99%

“…In this work we follow an alternative approach to the description of dissipative quantum noise which consists in directly modeling the superoperator in its Kraus represen- * Electronic address: garciama@tandar.cnea.gov.ar tation. The formalism of quantum operations to describe open systems, which is especially well adapted in the context of quantum information and quantum computing [10,11], has also been used for open quantum maps [12,13,14,15,16,17], which are quantum maps in the usual sense with some nonunitary noise that can be considered the effect of an interaction with some environment.…”

Section: Introductionmentioning

confidence: 99%

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Phase-space contraction and quantum operations

et al. 2005

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We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as "quantum phase space contraction rate" and which is related to a fundamental property of quantum channels: non-unitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attaractor-like structures is displayed.

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Spectral properties and classical decays in quantum open systems

Cited by 17 publications

References 52 publications

Pure state correlations: chords in phase space

Pure state correlations: chords in phase space

Relaxation Time of Quantized Toral Maps

Phase-space contraction and quantum operations

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